I sometimes think Japan is not a very eco-friendly country. When you buy a sweater at a department store, for example, they nicely wrap it with thin delicate paper, then put in a white plastic bag, and finally put it in a paper bag with the logo of the store printed.
That would be OK if it's a gift for someone. But if you buy it for yourself, you will probably throw away all those wrapping materials once you arrive home. What a waste!
At many supermarkets as well, they automatically give you plastic bags, so if you have your own shopping bags or you simply don't need them, please say: けっこうです。 Kekko desu. = No thank you.
To specify what you don't need you can say as follows:
袋は けっこうです。 Fukuro wa kekko desu = I don't need a bag, thank you.
はしは けっこうです。 Hashi wa kekko desu = I don't need chopsticks.
スプーンは けっこうです。 Supu-n wa kekko desu. = I don't need spoons.
At some supermarkets started to charge customers 2-10 yen for a single-use plastic bag. At those places they may ask you: 袋はお持ちですか。 Fukuro wa omochi desuka. = Do you have your own bag?
If you want one, please say: いいえ、一枚お願いします。 Iie, ichimai onegai shimasu. = No, can I have one?
By the way, the single-use plastic grocery bags are commonly called レジ袋（reｊi bukuro), because you can get those bags at the register. (＝reji)